lineCount_eq_pointCount — Mathlib

English

If HasPoints, then lineCount equality holds between counts at the dual configuration, mirroring HasLines.

Русский

При наличии HasPoints равенство подсчетов прямых и точек сохраняется в дуальной конфигурации, аналогично HasLines.

LaTeX

$$$\\text{lineCount}(L,p) = \\text{pointCount}(P,l)$ for corresponding duals$$

Lean4

theorem lineCount_eq_pointCount [HasPoints P L] [Fintype P] [Fintype L] (hPL : Fintype.card P = Fintype.card L) {p : P}
    {l : L} (hpl : p ∉ l) : lineCount L p = pointCount P l :=
  (@HasLines.lineCount_eq_pointCount (Dual L) (Dual P) _ _ _ _ hPL.symm l p hpl).symm

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